Error in solve.default(mat) Lapack routine dgesv system is exactly singular: Lapack routine dgesv: system is exactly singular: U[2,2] = 0

When attempting to utilize the solution() method on a singular matrix that lacks a matrix inverse, an error like this one will appear.

This lesson explains how to fix this mistake practically.

### How to Make the Error in solve.default(mat) Lapack routine dgesv system is exactly singular Again

Let’s say we use R to build the matrix shown below.

Let’s create a singular matrix

mat <- matrix(c(1, 1, 1, 1), ncol=2, nrow=2)

Now we can view the matrix

mat

[,1] [,2] [1,] 1 1 [2,] 1 1

Now imagine that we try to compute the matrix inverse using the solution() function.

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invert matrix try

solve(mat)

Error in solve.default(mat) : Lapack routine dgesv: system is exactly singular: U[2,2] = 0

The absence of an inverse matrix in the matrix we generated results in an error.

Please have a look at this Wolfram MathWorld article that provides ten examples of matrices without inverse matrices.

A matrix is considered singular by definition if its determinant is zero.

Before attempting to invert a particular matrix, you can find its determinant using the det() function:

Let’s compute the matrix’s determinant

det(mat) [1] 0

Our matrix’s determinant is zero, which explains why we encounter a problem.

## How to correct the issue

Simply making a matrix that is not single is the only way to correct this issue.

Consider using R’s solution() function to invert the matrix shown below:

Now we can generate a non-singular matrix

mat <- matrix(c(1, 7, 4, 2), ncol=2, nrow=2)

let’s view the matrix

mat

[,1] [,2] [1,] 1 4 [2,] 7 2

Now we can calculate the determinant of the matrix.

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det(mat) [1] -26

Let’s try to invert the matrix

solve(mat)

[,1] [,2] [1,] -0.07692308 0.15384615 [2,] 0.26923077 -0.03846154

The matrix is not singular, so when we invert it we don’t encounter any errors.

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